The linear source-filter theory of speech production ( Fant, G. (1970) Acoustic Theory of Speech Production; Stevens and House (1961)) is very useful for understanding speech synthesis and a foundation for acoustic analysis. I don't know if this is silly to ask, but I'm curious to know whether there are any alternatives to it. Or is it the major theory in the field of acoustic phonetics?
I think that source-filter theory is the major theory in the field of acoustic phonetics. Current textbooks on voice production and phonetics (e.g. Stevens 1998; Titze 2000) make use of the theory, and do not mention any radically different alternatives.
Source-filter theory is based on the same general mathematical framework that is used in signal processing research and control theory, fields which are highly developed with numerous practical applications. The method is more or less as follows [contributors with better math/engineering background feel free to edit this part]: the Laplace transform of an observed signal is treated as the product of a Laplace-transformed (actually occurring or ideal) input signal and one or more transfer functions (see the Wikipedia article for details). i.e.,
Output = Input x Transfer_function
As an input passes through each stage of a process, it is modified, and the effect of the modification is represented by a transfer function. Using this framework, acoustic phoneticians can model the speech production system in a way that separates the effects of the major components from each other. Then knowledge about simpler types of acoustic systems can be applied, and the models can be corroborated with empirical findings from physiological research.
Stevens, K. N. 1998. Acoustic Phonetics.
Titze, I. 2000. Principles of voice production.